UK and international copyright laws are complex, but as a rule of thumb they state that unless an individual is commissioned to shoot the video/stills, then that person owns the material. Even if he is commissioned to do the work, then the copyright can still be retained - it all depends on the agreement between the two parties.
What is almost certain is that, unless something in writing was agreed with the RAF prior to this shoot, or the RAF made crown copyright a pre-condition to getting the ride, then the rights for this footage are owned by fantaman. Thus, Beagle clearly has no idea about what he speaks, but hey, what's new?
The treasury and MoD are becoming altogether less agreeable about allowing the media and private individuals to depict the RAF roundel (even about use of the words 'Royal Air Force'), so it wouldn't surprise me if they come up with some silly pre-condition for shooting stills/video on such rides as this in the future.